1.According
to Stewart, what was the conclusion of Ruelle and Takens regarding the Landau or Hopf-Landau
scenario for the onset of turbulence?

2.What positive claim did
Ruelle and Takens make
regarding the onset of turbulence.

3.One can think about
several questions regarding the experiment on Couette-Taylor
flow that was performed by Harry Swinney and Jerry Gollub.What
was the physical arrangement of the experiment?What was the experimental procedure?What were the results, and how did
those results differ from expectations?

4.In what respects did
the experiments of Harry Swinney and Jerry Gollub support the claims of Ruelle
and Takens.

5.An important test of
the picture of Ruelle and Takens
is to exhibit a strange attractor in the results of a computer experiment on
some model of a dynamical system.Ruelle, Takens and Packard
proposed a scheme for using data for this purpose.Suppose that your data were the output of a computer solving
the Lorenz equations.How would
you organize and plot the data in order to exhibit the Lorenz attractor.

6.Likewise, how do you
organize and collect the data from real measurements of a dripping faucet in
order to show that there is a strange attractor in the dynamics.

7.What seem to be the
most important issues in this chapter for Stewart?

II.GLEICK, pp 121-153: STRANGE ATTRACTORS

1.The work of
David Ruelle and FlorisTakens is portrayed in GleickÕs
account as if it was an effort to invent the concept of a strange
attractor.In this connection, how
do they represent the behavior of a dynamical system (e.g., a turbulent fluid)?What aspects of the behavior of such a system and the occurrence
of chaos were they seeking to represent in a strange attractor?How does this relate to Stephen SmaleÕs horseshoe map?

2.What are
the attributes of the Lorenz attractor (see the figures on pages 28 and 140 and
the plate opposite page 114) that make it a strange attractor?

3.Consider
the Henon map (pages 149-150).How do we know that the representative
point of the system in the phase space has reached an attractor?And what is the attractor in that case?